ATLANTA, Georgia (CNN) -- Four months into a nationwide Salmonella Saintpaul outbreak, investigators Thursday still couldn't say where it originated.

The FDA announced it was lifting its ban on consumption of raw tomatoes, but hadn't ruled them out as the source. Hot peppers are also still being investigated, officials said.

In short, the inquiry continues, and one expert said this week that he understood the public's frustration.

"People are very used to the sort of 'CSI' thing where you put it into a computer and out comes the answer," said Ian Williams, chief of the Outbreak Net Team at the U.S. Centers for Disease Control and Prevention.

"In reality, sometimes we don't figure things out."

Williams and colleagues at the CDC and the Food and Drug Administration are continuing their pursuit of the culprits in the outbreak that sickened more than 1,200 people since April.

This salmonella problem is one of the most extraordinary Williams has seen, he said. It's the largest foodborne outbreak in the past decade, and the sources have so far been elusive. Unlike the E. coli outbreak in spinach in 2006, which was traced to packaged Dole brand baby spinach, tomatoes and peppers don't have barcodes. Learn about the differences between salmonella and E. coli »

Often people don't remember exactly what they ate and where that food came from.

"You have to pick good historians who know what they bought and where they bought it from," Williams said.

Tracking an outbreak origin is easier when cases are found in clusters of people who ate at the same event or restaurant, he said, because investigators can ask those people about a set menu of items. In this salmonella outbreak most clusters were small, most fewer than five people, he said, but the largest had 30 people.

In fact, recent investigations with clusters pointed to an association with jalapeño peppers, said Dr. Robert Tauxe, deputy director of the CDC's division of Foodborne, Bacterial and Mycotic Diseases, at a news conference Thursday.

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The CDC finds out about outbreaks through PulseNet, a national network of public health and food regulatory agency laboratories that the CDC coordinates. Through that system, a physician can submit isolated organisms from stool samples for analysis at a public health laboratory.

This enables researchers to get a "fingerprint" of that particular organism, which they then send to the CDC.

The New Mexico Department of Health informed the CDC of 20 salmonella cases on May 22, seven of which had Salmonella Saintpaul.

That number in the current outbreak has now reached 1,000 cases nationwide with the same Salmonella Saintpaul fingerprint -- a genetic marker normally seen in only 25 cases a year, Williams said.

The first step in figuring out what caused an outbreak like this is finding out what the cases might have in common.

Health inspectors sit down with 10 to 20 infected people and talk to them for about 90 minutes, asking where they went and what they ate in the week prior to getting sick. Investigators also present these people with a list of more than 200 food items commonly associated with outbreaks of a particular strain of bacteria.

In the case of the current salmonella outbreak, investigators found that 80 percent of this initial sample had eaten raw tomatoes in the week before they got sick, Williams said.

Further questioning showed close to 90 percent of those sickened consumed raw tomatoes, compared with about 65 percent of healthy people from the same areas, Williams said. Several of these people, though not the majority, had eaten at local or regional Mexican restaurants.

The team then decided to look at tomatoes and other things that go with tomatoes, like peppers and cilantro. Most recently, FDA dispatched a team to Mexico to investigate a packer that receives peppers from a number of farms.

Trevor Suslow, researcher at the University of California, Davis who studies perishable produce and bacteria, said the lengthy time span of cases with this Salmonella fingerprint, which extends from April to July, makes the outbreak especially complicated, as that seems to exclude any single tomato farm or region as the sole continuing source of contamination.

Although the case-control study showed a strong association between tomatoes and illness, "it's highly unlikely that any of those fresh tomatoes are currently on the market in any form," said Dr. David Acheson, associate commissioner for foods at the FDA, at Thursday's news conference.

The agency still discourages high-risk people -- elderly people, infants and those with impaired immune systems -- from eating serrano and jalapeño peppers. The lack of a similar ban for the general population reflects investigators' lack of certainty about the issue, Tauxe said. Read tips on food safety »